Finite element simulation of the DFD SAW motor is carried out in COMSOL Multiphysics using coupling of piezoelectric and solid mechanics modules is shown in Figure 5. 5.
Table 5. 1: Parameters used for FE simulation of the cylindrical shaft
Parameter symbol value Units
Frequency applied f 8.3165 MHz
Preload Fn 0.1199 N
Young's modulus shaft E1 169 GPa Young's modulus stator E2 172 GPa
Poisson's ratio shaft ν1 0.3 Poisson's ratio Stator ν2 0.345
Radius of shaft R 100 µm
Length ln 400 µm
Voltage applied V 100 V
Wavelength λ 400 µm
Mass of the shaft m 0.4 µg Static coefficient of friction s 0.45
Dynamic coefficient of friction d 0.15
Parameters involved in solving the SAW motor structure for translational motion is given in Table 5. 1. The table gives the information about young’s modulus and Poisson’s ratio of both the shaft and stator material. While it provides the information regarding the size and structure of each equipment involved in constructing the SAW motor. The application of the preload to the device keeps the shaft in high contact with the stators.
Figure 5. 5: Geometry of DFD SAW motor with cylindrical shaft used in the simulation.
The analysis starts with taking the device in the3D module of the Multiphysics software.
Initially, the dimensions of the stator are declared to make the device.
5.2.1 Creating the geometry of SAW motor
The 3D plane geometry of a delay line made by placing array of 4 IDT electrodes of aperture 400 µm (1 λ), width 100 µm (¼ λ) and thickness 0.2 µm on a LN substrate of width 400 µm (1 λ), length 2000 µm (5 λ) and height 800 µm (2 λ). The device is provided with a perfect matching layer to avoid reflections at the edges. A silicon (Si) shaft of length 400 µm and diameter of 200 µm is placed in the active region as shown in Figure 5. 5.
The properties of LN such as elastic coefficients, coupling coefficients, relative permittivity and material density are adapted from [84]. Aluminium is used for IDTs as it is lightweight and highly conductive. The material used for the shaft is Si. Table 5. 1 presents the list of parameters of shaft and stator used for simulating the device.
IDT Stator: LN
Slider at t = 0
Stator: LN
5.2.2 Multiphysics settings
The domain settings for the device is made by stating the stator as a piezoelectric element and IDTs and shaft are linear elements. Rayleigh wave reflection is absorbed through the PML boundary where each absorbing domain is set with the equation =1/(*f), where is absorbing condition and f is the frequency applied to generation of the wave.
The boundary settings in FE simulation are as follows. The bottom of the stator is fixed while the ends are terminated with perfect matching layers to avoid reflections. The Periodic boundary condition is applied to the aperture. The shaft and stator are defined as contact pair. The boundaries of the shaft are set free. Swept meshing was applied for all the domains.
The entire SAW motor system has to be divided into a number of individual subsystems before an analysis is carried out to understand the behaviour of the system [58]. Each basic units of the subsystems are called finite elements, which should neither overlap nor have gaps between each other. In order to solve the model, swept meshing was done for all the domains [60]. In this type of meshing a 3D device can be analysed properly, by making layer by layer mashing as shown in Figure 5. 6.
Figure 5. 6: FE model of the SAW motor with the cylinder as shaft after mesh.
5.2.3 Simulation of DFD SAW motor
The preload is applied to the shaft to increase friction at the contact surface with the stator.
As the generated Rayleigh SAW wave passes under the shaft, it makes a frictional contact with the bottom surface of the shaft. At the contact position, the wave puts frictional force on the shaft to move in the direction of the motion of the point on the surface of the stator.
The normal and tangential displacements of the point on the surface of the stator are on
IDT Stator: LN
Slider at t = 0
Stator: LN
average 3 nm and 8 nm respectively. The combination of the components of motion of the point makes the shaft to be drawn in the desired direction.
Figure 5. 7: Graph showing the velocity of the shaft in the normal direction.
Initially the shaft shows oscillation in the normal direction and the oscillation diminishes at the end of 5 µs as shown in Figure 5. 7.
Figure 5. 8: FE simulated picture of translational displacement of the cylindrical shaft.
This frictional force on the shaft drives the shaft in the direction opposite to the direction of propagation of SAW as shown in Figure 5. 8.
The cylindrical shaft is displaced 90 nm in 80 µs as shown in Figure 5. 9. The displacement of the shaft is smooth as seen in the plot. Hence the movement results in translational motion of the shaft in one axis i.e. -x-axis as shown in the simulated results in Figure 5. 9. If the excitation switched to IDTs on the other side, the movable object will start moving in the opposite direction i.e. in x-direction.
-4 -3 -2 -1 0 1 2 3
0 20 40 60 80
Velocity of the slider in normal direction (mm/s)
Time (µs)
IDT Stator: LN
Slider at t = 0
Stator: LN
Displaced slider
IDT Stator: LN
Displaced slider
Stator: LN
Slider initial position
Figure 5. 9: Graph showing the tangential displacement of the cylindrical shaft.
Hence, the shaft is able to make a motion in both positive and negative of x-axis which is the translational motion with a dual degree of freedom. The velocity of the shaft increases and saturates to 1.15 mm/s in 80 µs. The Figure 5. 10 shows that the shaft makes high contact pressure on the surfaces of the stators, visible as a line mark at the contact area.
Figure 5. 10: FE simulated picture for contact pressure generated at (a) bottom contact and (b) top contact of the shaft.